Kazhdan-Lusztig R-polynomials of permutations containing a 231 or 312 pattern

Abstract

We consider the Kazhdan-Lusztig R-polynomials, Ru,v(q) , indexed by permutations u,v of Sn, where u contains a pattern of type 231 or 232 and v is obtained from u by applying a transposition and an appropriate 3-cycle. We prove, using combinatorial techniques, that these polynomials are given by a closed product formula. The case of permutation which contain a pattern of type 321 follows from the others.